where P is the fundamental period, in samples, and
denotes the round-trip filtering on the string during one
period. (Placeholder values are given in the Faust listing so it will
compile and generate Fig.12.)

Figure 12:
Two strings coupled
by a general bridge impedance.

Note that the excitation only enters one of the string loops
in Fig.12. This corresponds, for example, to
plucking the string in the horizontal plane, say (the d1
loop), with the vertical plane (d2 loop) vibrating
``sympathetically''. More generally, the two loops may be excited by
varying amounts of the excitation signal, corresponding to a
physically inexact excitation plane.

where is the (real, positive) wave impedance of the string, and
denotes the bridge driving-point impedance (a positive-real
function of the Laplace variable ). The special case indicated in
the Faust listing above, , corresponds to ,
which is similar to the following simplified diagram (shown
in Fig.13) when g1 = g2
= g:

stringloop = (+ <: d2,d1 : + : *(0.5)) ~ *(g);

This simplified coupling algorithm runs about twice as fast as the
full algorithm (based on Faust benchmarks using the bench.cpp
architecture file).